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MA131 Fall 2013 Section 06 Quiz 6 Hint 1. Solve the following problem. Water is leaking out of an inverted conical tank at a rate of 11,500 cm3 /min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6 m and the diameter at the top is 4 m. If the water level is rising at a rate of 20 cm/min when the height of the water is 2 m, find the rate at which water is being pumped into the tank. (Round your answer to the nearest integer.) Hint: We know that Vcone = 31 πr2 h. Thus product rule. dV dt = π d(r2 h) 3 dt = π dh 3 (2rh dt + r2 dr dt ) with In a cone, r is proportional to h, which means r = αh. From h = 6m and 1 dh r = 2m, we can calculate α = 31 . Thus r = 13 h, and dr dt = 3 dt . Thus dV dt 2 can be written as π3 ( 2h3 dh dt + h2 dh 9 dt ). From the question, h is known here to be 2m and and we can calculate dV dt . dh dt is known to be 20cm/min We also notice that dV dt = V olumeChangein − V olumeChangeout , where V olumeChangeout is a known number of 11,500 cm3 /min. It will be easy to calculate the volume out speed. 1